Calculus Examples

$f (x) = \frac{\sin (x)}{\tan (x)}$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

Rewrite $\tan (x)$ in terms of sines and cosines.

$\frac{d}{d x} [\frac{\sin (x)}{\frac{\sin (x)}{\cos (x)}}]$

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (x)}{\cos (x)}$ .

$\frac{d}{d x} [\sin (x) \frac{\cos (x)}{\sin (x)}]$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Write $\sin (x)$ as a fraction with denominator $1$ .

$\frac{d}{d x} [\frac{\sin (x)}{1} \cdot \frac{\cos (x)}{\sin (x)}]$

Step 4.2

Cancel the common factor of $\sin (x)$ .

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Step 4.2.1

Cancel the common factor.

$\frac{d}{d x} [\frac{\sin (x)}{1} \cdot \frac{\cos (x)}{\sin (x)}]$

Step 4.2.2

Rewrite the expression.

$\frac{d}{d x} [\cos (x)]$

Step 5

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- \sin (x)$